Arnesh Sujanani

Efficient parameter-free restarted accelerated gradient methods for convex and strongly convex optimization

  • Arnesh Sujanani
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization Tags , , , , ,

    This paper develops a new parameter-free restarted method, namely RPF-SFISTA, and a new parameter-free aggressive regularization method, namely A-REG, for solving strongly convex and convex composite optimization problems, respectively. RPF-SFISTA has the major advantage that it requires no knowledge of both the strong convexity parameter of the entire composite objective and the Lipschitz constant of … Read more

    A low-rank augmented Lagrangian method for large-scale semidefinite programming based on a hybrid convex-nonconvex approach

  • Renato D.C. Monteiro
  • Arnesh Sujanani
  • Diego Cifuentes
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) method where the AL subproblems are solved by a novel hybrid low-rank (HLR) method. The recipe behind HLR is based on two key ingredients: 1) an adaptive inexact proximal point method … Read more

    An adaptive superfast inexact proximal augmented Lagrangian method for smooth nonconvex composite optimization problems

  • Arnesh Sujanani
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex proximal augmented Lagrangian (AL) subproblem obtained by an aggressive/adaptive choice of prox stepsize with the aim of substantially improving its computational performance followed by a full Lagrangian … Read more